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Dualities in population genetics: A fresh look with new dualities

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  • Carinci, Gioia
  • Giardinà, Cristian
  • Giberti, Claudio
  • Redig, Frank

Abstract

We apply our general method of duality, introduced in Giardinà et al. (2007), to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman’s type, as well as for models with finite population size.

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  • Carinci, Gioia & Giardinà, Cristian & Giberti, Claudio & Redig, Frank, 2015. "Dualities in population genetics: A fresh look with new dualities," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 941-969.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:3:p:941-969
    DOI: 10.1016/j.spa.2014.10.009
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    References listed on IDEAS

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    1. Etheridge, A.M. & Griffiths, R.C., 2009. "A coalescent dual process in a Moran model with genic selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 320-330.
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    Cited by:

    1. Frank Hollander & Shubhamoy Nandan, 2022. "Spatially Inhomogeneous Populations with Seed-Banks: I. Duality, Existence and Clustering," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1795-1841, September.
    2. Anja Sturm & Jan M. Swart, 2018. "Pathwise Duals of Monotone and Additive Markov Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 932-983, June.
    3. Kon Kam King, Guillaume & Pandolfi, Andrea & Piretto, Marco & Ruggiero, Matteo, 2024. "Approximate filtering via discrete dual processes," Stochastic Processes and their Applications, Elsevier, vol. 168(C).
    4. Belitsky, V. & Schütz, G.M., 2018. "Self-duality and shock dynamics in the n-species priority ASEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1165-1207.
    5. Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.

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